3914 | Phys. Chem. Chem. Phys., 2020, 22, 3914--3920 This journal is©the Owner Societies 2020

Cite this:Phys.Chem.Chem.Phys.,

2020, 22, 3914

First-principles comparative study of perfect anddefective CsPbX3 (X = Br, I) crystals†

R. A. Evarestov, a E. A. Kotomin,bc A. Senocrate, *b R. K. Kremerb andJ. Maier b

First principles Density Functional Theory (DFT) hybrid functional PBESOL0 calculations of the atomic

and electronic structure of perfect CsPbI3, CsPbBr3 and CsPbCl3 crystals, as well as defective CsPbI3 and

CsPbBr3 crystals are performed and discussed. For the perfect structure, decomposition energy into binary

compounds (CsX and PbX2) is calculated, and a stability trend of the form CsPbBr3 4 CsPbI3 4 CsPbCl3is found. In addition, calculations of the temperature-dependent heat capacity are performed and

shown to be in good agreement with experimental data. As far as the defect structure is considered, it is

shown that interstitial halide atoms in CsPbBr3 do not tend to form di-halide dumbbells Br2� while such

dimers are energetically favoured in CsPbI3, analogous to the well-known H-centers in alkali halides. In

the case of CsPbBr3, a loose trimer configuration (Br32�) seems to be energetically preferred. The effects

of crystalline symmetry and covalency are discussed, alongside the role of defects in recombination

processes.

Introduction

Halide perovskites have attracted great interest as light absor-bers for photovoltaic applications.1 Among these materials,hybrid organic–inorganic systems based on methylammonium(MA) and/or formamidinium (FA) lead iodide have shown thehighest performances in solar cell devices. Such hybrid compo-sitions, however, suffer from high instability under operation.One currently explored alternative is to move to the fully inorganicCsPbX3 (with X = I, Br), as these compounds could potentiallyfulfill both performance and stability criteria. However, manyaspects regarding the phase stability of these inorganic materials,as well as the influence of ionic defects on their properties haveyet to be thoroughly investigated experimentally and theoretically.Indeed, so far most of the theoretical studies on the atomic andelectronic structure of halide perovskites (inorganic as wellas hybrid organic–inorganic compositions) were focused ondefect-free materials.2–7 However, due to the low temperaturefabrication, and also due to the fact that these materialsare mixed ionic–electronic conductors,8–11 one could expect aconsiderable concentration of ionic defects in these systems.However, despite their potential role in influencing electronic

transport and device performance, there are only a few inves-tigations of point defects in Cs compounds,12,13 while there wasrecently a systematic study on hybrid perovskites.11,14,15 Notethat this aspect concerns not only mobile defects (couplingof ionic and electronic transport, interfacial redistributionprocesses), but also static ones (electronic carrier trappingand recombination). Even more, their importance lies in thefact that there is evidence showing that such ionic defects canbe photo-generated.16

A few studies published so far include first principlescalculations of native defects in MAPbI3,17 self-trapped holestherein,18 as well as native defects in CsPbI3.12,13,19 Recently,we investigated point defect formation and basic properties inCsPbI3 crystals from first principles calculations.20 It wasshown that interstitial iodine atoms tend to form I2

� dimers(‘dumbbells’) within the crystal structure, in agreement withprevious studies for MAPbI3,17,18,21 and with the well-knownsituation in alkali halides.22–26 In alkali halides, the X2

� dumbbells(called H centers) can be created under UV light irradiation.A similar situation, but under visible light irradiation, has beenhypothesized to be the cause for the light-enhanced ion conduc-tion reported in MAPbI3.16 Thus, studying interstitial halide ions isimportant to understand charge transport properties in halideperovskites, both in the dark and under illumination.

In this paper, we continue our first principles calculations20

by calculating the formations energies of CsPbI3, CsPbBr3 andCsPbCl3 from their parent binary compounds, and include alsovibrational effects by performing heat capacity calculations. Wecompare these with experimental heat capacities, showing an

a Institute of Chemistry, St. Petersburg State University, Petrodvorets, Russiab Max Planck Institute for Solid State Research, Stuttgart, Germany.

E-mail: alessandro.senocrate@googlemail.comc Institute of Solid State Physics, University of Latvia, Riga, Latvia

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9cp06322f

Received 22nd November 2019,Accepted 25th January 2020

DOI: 10.1039/c9cp06322f

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excellent agreement. We also expand our study of the defectivestructure of Cs-based halide perovskites by considering inter-stitial bromide ions in cubic CsPbBr3. We show that theformation of Br2

� dumbbells is energetically unfavorable, incontrast with the situation in CsPbI3. Instead, the energeticallymore favorable configuration for an interstitial bromide is aloose trimer (Br3

2�) (Fig. 1). Calculations of the one electronenergies show that one electron levels of the interstitial defectsin both CsPbI3 and CsPbBr3 lie in the middle of the bandgap,thus may act as traps for photo-generated carriers.

Theoretical methods

Our first-principles periodic calculations were performed inthe frame of the hybrid DFT PBESOL0 implemented in theCRYSTAL17 code.27,28 This is a hybrid version of PBE exchange–correlation (XC) functional with 25% of Hartree–Fock exchange andrevised for solids PBESOL29 XC functional instead of the PBE XCfunctional. The hybrid exchange correlation functionals allow us toobtain a much better agreement with experiments concerning theband gap of perovskite materials.

Spin–orbital (SO) interactions were neglected in our calcula-tions, since we expect these to have negligible influenceon defect formation energies as well as phase stability. Onthe other hand, SO interactions significantly affect the bandgap results. It has been shown for CsPbI3

17 that includingSO interactions leads to the increase of the valence band topby 0.2 eV and to the decrease of the Pb-based conduction band

bottom by 0.8 eV. For CsPbBr3 and CsPbCl3, SO correctionswere extracted from LMTO calculations.30 Taking these intoaccount, our calculations are found in good agreement withexperimental band gaps.

Gaussian atomic orbitals31 were used to expand the crystallineBloch functions. The interaction between the core electrons andthe valence and sub-valent electrons in iodine, lead and cesiumatoms and the valence electrons was described by means ofeffective core pseudopotentials.

The Brillouin zone (BZ) sampling was performed with8 � 8 � 8 k-point meshes generated according to the MonkhorstPack scheme.32 Kohn–Sham equations were solved iteratively toself-consistency within 10�8 eV. Full geometry optimization wascarried out both in perfect and defective crystals calculations.The Mulliken analysis was used for effective atomic charges.

In the point defects calculations, the supercell model33,34 wasused and a supercell composed by 8 primitive cells (2 � 2 � 2)was chosen (the main conclusions were confirmed by also usinga 16 primitive cells supercell). In the perfect cubic CsPbX3

crystal, three Wyckoff positions of the space group Pm%3m withthe simple cubic lattice are occupied: Cs 1b (0.5,0.5,0.5), Pb 1a(0,0,0), X (= I, Br) 3d (0.5,0,0). The neutral iodine and bromineatoms Xi were initially placed into the interstitial c-position withthe coordinates (0.25, 0.25, 0) in the supercell and allowed tomove, in order to find the configuration with the minimum totalenergy. All symmetry restrictions were lifted in the calculationsof the defective crystals, in order not to constrain the optimiza-tion of lattice parameters and atomic coordinates.

The Xi formation energies Ef were calculated using thefollowing relation:

Ef = Edef � (Eperf + Ui) (1)

where Eperf is the energy of a perfect supercell, Edef that of thesupercell with a defect, and Ui is the chemical potential of a Xatom (1/2 of the total energy of X2 molecule in a gas phase).

The CsPbX3 decomposition energies into binary compoundswere taken from total energies of binary parent compounds(Table 1)

Edec = E(CsPbX3) � [E(CsX) + E(PbX2)], (2)

Note that CsX has a cubic structure for all three halides,whereas PbI2 has trigonal symmetry (space group P%3m1) withone formula unit per primitive unit cell, in contrast to PbBr2

and PbCl2 which are orthorhombic (Pnam) and contain fourformula units per unit cell.

Fig. 1 Schematic view of the perfect CsPbI3 and CsPbBr3 crystals, andof the structures including interstitial halide atoms, before and afterstructural relaxation.

Table 1 Calculated basic properties of bulk parent binary crystals: a0 cubic lattice constant, q effective atomic charges (e), UCs, UPb are extracted Cs, Pbchemical potentials (a.u.). Chemical potentials of Cl, Br, I were calculated in ref. 20

Space group Z a0, b0, c0 expt36 (Å) a0, b0, c0 calc (Å) |q| (e) UCs, UPb (a.u.)

CsI Pm%3m 1 4.57 4.66 0.99 �20.011333CsBr Pm%3m 1 4.29 4.39 0.99 �20.023117CsCl Pm%3m 1 4.12 4.19 0.99 �20.052488PbI2 P%3m1 1 4.56, 6.78 4.69, 6.57 0.84, �0.42 �3.659705PbBr2 Pnam 4 8.06, 4.73, 9.54 8.01, 4.75, 9.56 1.12, �0.54, �0.58 �3.684755PbCl2 Pbnm 4 7.61, 4.53, 9.03 7.54, 4.51, 9.03 1.32, �0.63, �0.69 �3.745345

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The heat capacity at constant volume (Cv) was calculated in aharmonic approximation according to ref. 34 and 35

CvðTÞ ¼1

Nk

XNk

k

XNni¼1

CviðT ; kÞ;

CviðT ; kÞ ¼ kBh

kB

niðkÞT

� �2exp h=kBð ÞniðkÞ=T½ �

exp h=kBð ÞniðkÞ=T½ � � 1f g2(3)

where kB is the Boltzmann constant, h the Planck constantand i the number of phonon modes with frequency ni over Nnbranches. As one can see from eqn (3), Cv calculations requiresummation over k set in the Brillouin zone. Our phononcalculations are made by the so-called direct method whichrequires the supercell-zone folding transformation to includein (3) non-zero k-points. We used three sets: only G-point, 8 and16 k-points. These sets are discussed in ref. 29 and generatedby supercell-zone folding transformation for the simple cubiclattice. More methodological details have been given in ourprevious study.20 It has been shown therein that the chosenhybrid functional reproduces well both the atomic structureand band gap of three related materials CsPbI3, CsPbBr3 andCsPbCl3. The calculated lattice constants deviate by less than1% from the experimental values. The effective ionic chargesfor Cs ions are always close to +1e. Pb shows some covalencydue to chemical bonding with halides, the charges of which are�0.62e for I and �0.65e for Br ions. This indicates, as expected,that CsPbBr3 shows a more pronounced ionic character withrespect to CsPbI3.

Experimental methods

The heat capacities at constant pressure (Cp) of polycrystallinesamples of CsPbBr3 and CsPbI3 were measured in the tempera-ture range 0.4 K r T r 100 K employing the relaxation methodusing a Physical Property Measurement System (PPMS,Quantum Design). The samples were thermally coupled withApiezon N grease to the sapphire platform. The heat capacitiesof the platform and the vacuum grease were measured before inseparate runs and subsequently subtracted from the total heatcapacities. The comparison between theory and experiments isbased on the assumption that the calculated heat capacities atconstant volume (Cv) do not differ significantly from theexperimental heat capacities measured at constant pressure (Cp).These two values are linked by the relation:37

Cp(T) = Cv(T) + E(T)�T (4)

E(T) = av2(T)�B�Vmol (5)

where av(T) is the volume coefficient of thermal expansion,B the bulk modulus and Vmol the molar volume at 0 K. Basedon eqn (5), we therefore expect negligible differences betweenCp and Cv, especially at low temperatures.

To fit the experimental heat capacities, a standard Debyebehavior (with its characteristic Debye temperature YD) has beeninitially considered. However, the experimental curves deviatequite strongly from this standard behavior, therefore this simpleapproximation has been complemented with the Einstein modes(corresponding to maxima in the phonon density of states due toacoustic phonon modes with low dispersion at zone boundaries,typically originating from vibrations of heavy atoms withincompounds38,39). These Einstein modes are generated with 2parameters, a characteristic temperature (YE) indicating theposition of the maximum in the phonon density of states, and aweight (WE) representing the fraction of atoms participatingin this behavior.

Results and discussion

The calculations presented here consider primarily the cubicstructure of CsPbI3 and CsPbBr3 crystals. It is known experi-mentally that these cubic structures are found above 400 K and580 K, respectively, whereas below these temperatures thecrystals are orthorhombic.40 (Note that, in the case of CsPbI3,significant distortions from the ideal cubic perovskite structureremain even above the transition temperature).40 This structuralinstability is confirmed by our calculations of the phonons incubic CsPbBr3, which show imaginary frequencies at the R pointof the Brillouin zone. The reason for the choice of the cubic cellrelies on the fact that, especially for CsPbI3, the orthorhombicphase has a large bandgap, and thus is not of interest forphotovoltaic applications. Owing to this, many efforts have beendevoted to the stabilization of the perovskite (distorted cubic)structure at room temperature.41 Nevertheless, as presentedlater, comparison with the orthorhombic crystal structure willalso be given, in particular concerning structural parameters andformation energies.

Let us start by discussing the perfect structure. Our calcula-tions, as already shown previously,20 are able to satisfactorilycapture both the crystal phase and the electronic structure ofCsPbI3, CsPbBr3 and CsPbCl3. From this basis, we move tocalculate the decomposition energies of all these compounds(in the cubic phase) into the binary parent materials CsX andPbX2 (eqn (2)). Unsurprisingly, these energies are rather small(see Table 2): 0.23 eV, 0.26 eV and only 0.02 eV per formula unitfor I, Br and Cl respectively. According to our calculations, the

Table 2 Phase energetics of cubic CsPbX3 crystals into binary compounds calculated through total energies. Subscript pro represents the products andpre the precursors. Edec indicate the decomposition energies from eqn (2)

Product (Pm%3m) Epro (a.u.) Precursors Epre (a.u.) Spre (a.u.) Edec (a.u.) Edec (eV)

CsPbI3 �57.847 CsI + PbI2 �31.402 �26.436 �57.838 0.0086 0.23CsPbBr3 �63.725 CsBr + PbBr2 �33.359 �30.357 �63.715 0.0094 0.26CsPbCl3 �68.417 CsCl + PbCl2 �34.925 �33.491 �68.417 0.0007 0.02

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chloride perovskite is expected to be the least stable of all threecompounds, while bromide and iodide show comparablestabilities. The strong deviation of the formation energy ofCsPbCl3 from the trend may be connected with the more ionicnature of this compound (compared with the other two ones)and will require a more detailed study. The lack of experimentalobservations on the stability of these compounds makes anyfurther conclusion at the moment unreliable.

We have also performed the calculations for the orthorhombicCsPbI3, CsPbBr3 and CsPbCl3, which now have four formula unitsper unit cell. Table 3 shows the obtained decomposition energies,which are larger than for the cubic crystal, consistently with theorthorhombic phase being more stable at the temperature repre-sented by the calculations. The value for the decompositionenergy of orthorhombic CsPbI3 also agrees well with recentexperimental work,42 where the formation enthalpy of the phasefrom its solid halide precursors was estimated to be �0.18 eV.

In further agreement is the fact that the experiments showthe orthorhombic phase being more stable than the cubic one,albeit the experimental difference between the formation energyof cubic and orthorhombic CsPbI3 (0.15 eV)42 is found to behigher than our calculated one (0.08 eV).

In addition, we have calculated and measured the heat capacityof CsPbI3 and CsPbBr3 in the cubic crystal structure. Fig. 2aand b shows the experimental and theoretical dependence ofthe heat capacity on the temperature. The experimental curves

tend to reach the classical limit given by the Dulong–Petit law(Cp = 3NA�R, with R being the molar gas constant and NA is thenumber of atom in the formula unit). This approximation yieldslimit values of B125 J (mol K)�1 for CsPbX3. The calculationresults depend on the number of k-points (Nk) used for thephonon calculations. Using only the gamma point (the simplestapproximation) leads to a considerable underestimate (B20%)of the heat capacity at high temperatures.

An increase of the number of k-points reduces the discrepancy,with 16 k-points providing sufficiently good agreement withexperiments. Preliminary calculations also show that moving awayfrom the cubic structure to consider an orthorhombic distortionyields no substantial difference in the calculated heat capacityvalues. This finding indicates that the crystal phase does notstrongly affect the thermal behavior. More detailed calculationsare on the way. The experimental heat capacities were also plottedin the coordinates useful to check for deviations from the Debyeapproximation (o p k), with Cp vs. T 3 at low temperatures.As shown in Fig. 3, the peak at low temperatures in the quantityCP/T 3 indicates deviations from Debye behavior, as demon-strated by the comparison with the heat capacities (red solidlines) calculated assuming constant Debye temperatures asindicated. Such peaks typically result from maxima in thephonon density of states originating from acoustic phononmodes with low dispersion at the zone boundaries, originatingfrom vibrations of heavy atoms in the compounds (see e.g.ref. 38 and 39).

We also noticed that the very low temperature behavior canbe sample-dependent, likely due to structural defects and/or

Table 3 The same as Table 2 for orthorhombic (Z = 4) CsPbX3 crystals (energies are given per formula unit)

Product (Pnma) Epro (a.u.) Precursors Epre (a.u.) Spre (a.u.) Edec (a.u.) Edec (eV)

CsPbI3 �57.849 CsI + PbI2 �31.402 �26.436 �57.838 0.011 0.30CsPbBr3 �63.726 CsBr + PbBr2 �33.359 �30.356 �63.715 0.011 0.30CsPbCl3 �68.419 CsCl + PbCl2 �34.925 �33.491 �68.417 0.002 0.08

Fig. 2 Theoretical and experimental temperature dependence of the heatcapacity for (a) CsPbI3 and (b) CsPbBr3. Calculations have been performedon the cubic structure for different numbers of k-points (Nk, indicated inthe figure).

Fig. 3 Experimental heat capacity of (a) CsPbI3 and (b) CsPbBr3 dividedby T3. The red solid lines represent the Debye heat capacity assuming Debyetemperatures of 109 K for CsPbI3 and 102 K for CsPbBr3, respectively.

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impurity which are difficult to control during the liquid-basesynthesis. This aspect is discussed in more detail in the ESI.†

Let us now turn to important points concerning the model-ling of the defective structure, namely the effect of the insertionof an interstitial halide in CsPbI3 and CsPbBr3. Fig. 4 shows theinitial and final crystalline structure for the interstitial halideatoms inserted into the cubic crystals. In the case of CsPbI3,introduction of an interstitial I leads to the formation of an I2

�

dumbbell through interaction with one of the neighboringI ions. This process is accompanied by a considerable distor-tion of the lattice surrounding the defect (Fig. 4b), not onlylocally but also at long range (Table 4).

We found in our previous study20 that the dumbbell(H center) formation is energetically favorable (Ef = �0.37 eV),notwithstanding the inclusion of the interstitial I atom atlow temperatures. The I2

� bond distance within the dumbbell(3.32 Å) is slightly shorter that in a free I2

� ion (3.35 Å), as alsoobserved for the H centers in alkali halides.22 In addition, thedumbbell formation causes a charge redistribution that leavesan almost identical charge on the two constituting I atoms (0.35eand 0.42e, with a small difference due to lattice distortions).Our previous calculations20 predicted also that the formation of

larger aggregates e.g. trimers I32�, is possible, but energetically

less favorable (by 0.62 eV). A comparison with CsPbBr3 reveals avery different situation (Fig. 4d): the lowest in energy configu-ration after incorporating a neutral interstitial Br is a loosetrimer, where distances between a central Br atom and twonearest halides are considerably larger (by 0.11 A and 0.18 A)than in a typical Br2

� dimer as found in alkali bromides (thecomparison with the dimer is carried out due to the lack ofliterature data on bromide trimers).22,26,43

The formation energy of this complex defect is substantiallylarger (by 0.59 eV) than for the I2

� dimer. In the trimer, acharge of 1.5e is spread over all three participating Br atoms.Considering that, due to some covalent character, the charge ofthe regular host Br ions (not participating in the trimer) is�0.65e, this indicates that the trimer is best denoted as Br3

2�.To check the influence of the supercell size on the resultsobtained, we also performed time-consuming calculationsdoubling the supercell size (16 primitive unit cells insteadof 8). The main conclusions are maintained, i.e. the H centerformation energy is lower for CsPbI3 than CsPbBr3 (Br2

� andI2� formation energy difference is 0.51 eV for a supercell of 16

unit cells). The X–X distance and Mulliken atomic chargesare practically the same for supercells composed of 8 and 16primitive cells. This substantial difference in behavior betweenthe H center formation in CsPbI3 and CsPbBr3 could be relatedto the difference in the crystalline structure of the parent PbX2,as PbI2 has a rhombohedral P%3m1 symmetry (one formula unitper unit cell), while PbBr2 takes an orthorhombic Pnam spacegroup (4 formula units per unit cell). As a consequence, thebromide ion sublattice has 4 atoms in the unit cell and theirinteratomic interactions become stronger in the perfect crystal,making the formation of a Br2

� dumbbell more difficult whenthe interstitial bromide atom is inserted.

Considering the potential importance that this material hasfor photovoltaic and optoelectronic applications, we calculatedpositions of the energy levels of the interstitial defects in bothcrystals and found that in both cases these lie in the middle ofthe band gap (0.7 eV and 1 eV above the valence bandmaximum in CsPbI3 and CsPbBr3 respectively, with calculatedbandgaps of 1.7 and 2.1 eV20).

Due to their energy levels in the middle of the band gap,these defects could trap both electrons and holes. However, assuch states are unstable (e.g. dimer or trimer dissociates after

Fig. 4 Comparison between the structure of CsPbI3 and CsPbBr3 withthe addition of an interstitial halide atom. Structure (a) and (c) before and(b) and (d) after optimizing geometry. For simplicity, only a schematicrepresentation of a single unit cell containing the defect is given, but thecalculations have been performed on a 2 � 2 � 2 supercell. Note that theadditional neutral iodide in CsPbI3 interacts during geometry optimizationwith regular lattice iodide ions, forming a dumbbell. A different process(trimer formation) takes instead place for CsPbBr3.

Table 4 Structural properties and energies involved in the insertion of an interstitial halide defect in CsPbI3 and CsPbBr3 (calculated in a 40 atomsupercell with full geometry optimization and without fixing symmetry). a0, b0, c0, and the angles are the structural parameters after geometryoptimization (values in brackets correspond to the perfect crystal); q are the atomic charges on the various atoms in the perfect crystals; Ef is the defectformation energy for a halide interstitial insertion (eqn (1)); R, q are the distance and charge of a halide dimer (X2

�); DR is the distance change afterstructural optimization between the introduced interstitial Xi atom and 3 nearest neighbors X1, X2, X3; q are the atomic charges of such halide ions

CsPbI3 CsPbBr3

a0, b0, c0 (Å) 12.630, 12.703, 12.595 (12.660) 11.911, 11.799, 11.988 (11.880)Angles (1) 90.09, 89.76, 89.01 (90) 89.95, 89.85, 90.02 (90)qCs, qPb, qX (e) 0.99, 0.85, �0.62 0.99, 0.95, �0.65Ef (eV) �0.37 eV +0.22 eVR, q (Å, e) 3.35, �0.50 2.96, �0.50DR (Xi, X1, X2, X3) (Å) �0.03, +0.48, +0.52 +0.11, +0.18, +0.95q (Xi, X1, X2, X3) (e) �0.35, �0.42, �0.61, �0.63 �0.39, �0.54, �0.56, �0.63

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trapping an electron), these defects may not strongly affect theefficiency of the recombination processes in photovoltaicdevices. The same is true for halide vacancies and Vk centers,but because they form shallow energy states.

Conclusions

In conclusion, we have confirmed the high quality of our hybridDFT PBESOL0 calculations, not only by finding excellent agree-ment with experimental lattice parameters and properties, butalso by obtaining reasonable values for formation energies andheat capacities in CsPbX3 (X = Cl, Br, I).

The decomposition energies of CsPbX3 crystals in both cubicand orthorhombic phases were estimated using the results ofPBESOL0 calculations of binary parent CsX and PbX2 crystals.The perovskite stability sequence was found as CsPbBr3 4CsPbI3 4 CsPbCl3 for both crystalline phases.

The frozen phonon method was applied to obtain the tempera-ture dependence of the heat capacity in the cubic phase. The goodagreement obtained with the experimental data confirms the highaccuracy of our calculations.

Concerning the defective structure, our first principles super-cell calculations on CsPbBr3 show that the interstitial Br atoms(unlike the interstitial I atoms in CsPbI3) do not form a Br2

� dimer(commonly known as H center in alkali bromides),44 but rather aloosely bound trimer (Br3

2�). Simple chemical arguments indicatethat, due to the much higher polarizability, iodine atoms andions are expected to form higher aggregates (e.g. polyiodides).The same situation is not expected (at least to a similar extent)in bromides.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We thank R. Merkle for numerous fruitful discussions andG. Siegle for experimental assistance. This study was partlysupported by the M-ERA-NET project SunToChem (EK). Calcu-lations were performed using computational facilities ofSt. Petersburg State University and Max Planck Institute forSolid State Research. Open Access funding provided by the MaxPlanck Society.

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